Chapter 12. Gödel versus Wittgenstein and the Paraconsistent Interpretation

  1. Francesco Berto

Published Online: 23 JUL 2010

DOI: 10.1002/9781444315028.ch12

There's Something about Gödel: The Complete Guide to the Incompleteness Theorem

There's Something about Gödel: The Complete Guide to the Incompleteness Theorem

How to Cite

Berto, F. (2009) Gödel versus Wittgenstein and the Paraconsistent Interpretation, in There's Something about Gödel: The Complete Guide to the Incompleteness Theorem, Wiley-Blackwell, Oxford, UK. doi: 10.1002/9781444315028.ch12

Publication History

  1. Published Online: 23 JUL 2010
  2. Published Print: 6 NOV 2009

ISBN Information

Print ISBN: 9781405197663

Online ISBN: 9781444315028

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Keywords:

  • Gödel versus Wittgenstein and the paraconsistent interpretation;
  • Gödel, definitely the logician of the millennium;
  • Wittgenstein's remarks on foundations of mathematics;
  • trait between “early” and so-called “later” Wittgenstein - from Tractatus logico-philosophicus;
  • Wittgenstein's remarks on Incompleteness Theorem - his attempt to separate what he calls the “proof”;
  • implausible Wittgenstein - with his remarks on the Incompleteness Theorem;
  • Journal of Philosophy to Dialectica and Erkenntnis;
  • Wittgenstein, being coherent - bold move of rejecting standard distinction between theory and metatheory;
  • the single argument - applying the First Incompleteness Theorem to theory that captures our intuitive, or naïve, notion of proof;
  • “semantic prose” on First Theorem - attacked by Wittgenstein, truth of Gödel sentence established in metatheory

Summary

This chapter contains sections titled:

  • When geniuses meet …

  • The implausible Wittgenstein

  • “There is no metamathematics”

  • Proof and prose

  • The single argument

  • But how can arithmetic be inconsistent?

  • The costs and benefits of making Wittgenstein plausible